Factions is not a formally defined term in Ryzom, so it can be rather ambiguous. It may have the following meanings:
In informal speech, factions usually refers to the higher powers: the Kami and the Karavan. Most often when people use the term factions, this is what they refer to.
This use matches general online games lingo because most games make players choose between two opposing sides referred to as the two factions.
In Ryzom specifically, until recently Faction points could only be earned with the Kami and the Karavan, and Faction PvP was always Kami versus Karavan. This is no longer the case (see below) but the terminology has stuck.
Though it is often used so informally, no official source refers to the Kami and Karavan as the factions; they are referred to as the higher powers, the religions or the cults.
In addition to the higher powers, factions may also refer to the 4 nations; the Fyros, Matis, Tryker and Zoraï. The nations may also be referred to as the races or the civilizations.
This use stems from the Faction points and Faction PvP, the only two places where the term faction is used in the game.
Thus this would seem to be the most formally correct use of the term factions, however it is rarely used this way in conversation.
From the very beginning, the players who didn't align with any faction and thus remained neutral have often been referred to as the third faction (in the case of the higher powers) or the fifth faction (in the case of the civilizations). It's a matter of opinion whether neutrality is actually a faction or rather the lack of faction.
This issue was only complicated further when different kinds of neutral were implemented: Hominists who are friendly with all nations, Marauders who are hostile to all nations, Theists who are friendly with both higher powers and Antitheists who are hostile to both higher powers. All those groups also get their own Faction PvP icon.
And of course, there are still the remaining neutrals who don't fall into any of those groups. So all in all there are now 6 different neutral factions.
Recently, a new Ranger rite has been created [1].
This use of the term factions stems from the concept of fame, and defines a faction as "any group that players can obtain fame with". The term is rarely used this way in practice.
Players can obtain fame with the 2 higher powers, the 4 nations and the 51 tribes. However, players can only align themselves with a higher power and a nation.
Lastly, factions may be used to simply refer to the different sides in whatever conflict is currently playing.
For example, the Kitin might be referred to as a faction, even if players can't get fame with them nor align with them.
The Marauders also were often referred to as a faction long before players could support them